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Berkeley University was one of the first universities to be sued for sexual discrimination. In the fall of 1973, 12,763 people applied for admission through the Graduate Admission Office. 8,442 of the applicants were males, and 4,321 were females. 44% of the males were successful, but only 35% of the females were admitted.[1]

We can see Simpson's paradox in that in 4 of the cases a higher ratio of females were admitted and the other two the difference is not great. However, this ratio does not accurately represent the overall ratio between females admitted and males admitted—in fact, a higher ratio of males were admitted overall, a reversal of most of the ratios found in the individual majors.

The cause of the paradox can be found by the number of applicants.

A

B

C

D

E

F

Overall

Male

825

560

325

417

191

373

2691

Female

108

25

395

375

393

341

1835

Of the 1,835 female applicants 1,504, or 82%, applied for courses in which ~33% (or less) applicants were admitted. Of the 2,691 male applicants 1,385, or 51.5%, applied for courses in which ~ 66% applicants were admitted. Berkeley won the case.